Three-axis gimbal-based beam director and receiver systems in general provide a hemispherical field of regard and in some instances a hyper-hemispherical field of regard, which refers to a field of regard greater than 180 degrees.
Borrowing from astronomical telescopes, it is a requirement that the telescope be able to point anywhere in the sky. In order to do that, a two-axis system is employed that points the telescope utilizing an azimuth gimbal that rotates the telescope around in a horizontal direction, commonly known as dome rotating. The other pointing axis is the elevation axis, which points up from the horizontal azimuth axis such that it is possible to direct the telescope to point anywhere within the hemisphere.
The problem in controlling such a telescope is the ability to point. at a position in space that is located straight up (zenith) or straight down (nadir). The difficulty to point in these directions and to be able to maneuver the telescope about these straight up and down directions is called gimbal lock, in some instances referred to as zenith lock.
Taking, for instance, if one is looking towards the zenith where one is pointing straight up, if one spins in azimuth utilizing the azimuth gimbal, the point of the optical axis of the telescope does not move because as the azimuth gimbal moves, the beam pointing is in the same direction. Thus, while the azimuth gimbal provides motion in the azimuth direction, one is still spinning around a fixed point in space. As a result, the ability to control a second direction is lost when pointing straight up or straight down.
The result is that if one is trying to track an object that is directly overhead or close to overhead, the azimuth gimbal is ineffective to move the telescope pointing direction.
By way of example, consider some other point such as, for instance, a satellite or an object moving perpendicular to the direction that the elevation gimbal provides. If the target is moving perpendicular to the azimuth there is no way to track the movement of the object when it is at the zenith of the system. Thus, when a target is at the zenith, one cannot track it by spinning the azimuth axis. Similarly, when the object is close to the zenith or nadir directions, the azimuth gimbal has to spin at increasingly faster rates to provide ever-diminishing amounts of motion until at zenith, no motion is provided by the azimuth gimbal even with rates approaching infinity.
The result is what is called “gimbal lock” in that one is locked to motion in only one direction. When looking in this direction, one cannot track or stabilize in other directions. As a result, if one is tracking an object that is at or near the zenith of the system, one cannot track in a direction that is orthogonal to the elevation axis.
Moreover, with respect to line-of-sight stabilization, one normally tries to stabilize in two directions. However, if the object to be stabilized on is directly above or below the gimbaling system, one can only stabilize on one axis or equivalently, in only one direction. As a result one loses the ability to stabilize the line of sight of the system along a second direction.
In summary, gimbal lock fundamentally eliminates the ability to track or stabilize objects that are at or close to the zenith or nadir of the system. This problem of gimbal lock is a well-known problem and in the past three-axis systems were utilized instead of two-axis systems to solve the gimbal lock problem. If one has an additional gimbal either inside or outside the two-axis system, one can eliminate gimbal lock by choosing configurations or control algorithms that ensure that 2 axes are never aligned when one of the 3 rotation axes is aligned with the line-of-sight direction. This would result in only a single axis of control.
In such systems the azimuth and elevation axes are always perpendicular to each other. There are, however, occasions when using a third axis on the inside or outside of the two-axis system, the third axis can be lined up with one of the two other axes depending on where one is pointing.
However, if one is not careful with the control algorithms one can obtain a situation in which the orientation of the third axis can line up with one of the two other axes. Where one has an accidental lineup, one only has two axes available, which again reverts to the two-axis gimbal lock problem.
Thus, one wants to establish the case where when providing for the three different axes, one avoids the situation in which two of the axes line up one with the other while any one of the axes is aligned along the line-of-sight.
While control algorithms exist to make sure that the third axis does not result in the lining up of any two axes, installing a third gimbal in the past has added increased weight and considerably more mechanical complexity. Thus, if one provides a third gimbal within the other two gimbals, the gimbal system tends to be heavy and the positioning is not particularly rapid due to the mass of the third gimbal. Also one needs big torque motors and low-friction bearings to obtain quick stabilization or pointing response. Thus, these three-gimbal systems suffer from reduced bandwidth and increased inertia. Also, providing a third gimbal occupies a considerable amount of volume.
What is therefore required is a system for providing a low mass, high-speed third axis that does not require additional volume and achieves high-speed tracking and pointing with increased bandwidth.
More specifically, the third-axis gimbal described above is characterized by slower accelerations and lower bandwidths for the outer gimbal. The accelerations are angular accelerations, which refer to how fast one can rotate an object about the axis. The bandwidth is the frequency by which one can track disturbances. If one has random disturbances such as those associated with aircraft, one would have random motions of the airframe that may, for instance, be caused by vibration. A tracking system must be able to cancel these random motions by providing a system with high bandwidth, meaning a system that can compensate for high-frequency disturbances.
Thus, if one has high bandwidth one can track something that is uttering at a high frequency, whereas if one has a low bandwidth, one can only track something or stabilize the line of sight if the apparatus base or other components are vibrating very slowly.
It is noted that if one has enough power and a strong-enough motor, one can drive a three-axis system to accommodate fast jitter, albeit at the expense of weight, size and power.
Moreover, while it is theoretically possible in conventional three-axis mechanical gimbaling configurations to push the gimbal lock to 90 degrees away or to some other point where gimbal locking is not a problem, i.e., to move the gimbal lock position to regions or locations that are not of interest, such gimbal lock positioning is not always possible.
In particular, one would like to have line-of-sight stabilization about the pointing direction utilizing high-bandwidth, low-inertia line-of-sight stabilization around any point position within the hemisphere. Thus, if one is pointing at any arbitrary angle, one needs two degrees of control, typically one up and down and the other left and right, i.e., one vertical and one horizontal. Thus, no matter where one points, one needs up-down and left-right stabilization.
When providing a three-axis system, there is a second consideration. If one can provide orthogonal axes that are high-bandwidth, low mass and truly orthogonal to each other, this configuration provides the best pointing direction control. Assuming that wherever one is looking within the hemisphere, one has two axes of control that are truly 90 degrees to each other, one can provide simplified pointing control.
The advantage of having two orthogonal control axes about the pointing position is that it allows one to decouple the control system. Rather than having a two-dimensional controller, one can have two one-dimensional controllers, one for each control axis.
Thus, instead of trying to control two axes simultaneously, one seeks to control them separately, which minimizes the mathematical complexity. The result is that rather than having a controller that is moving two axes simultaneously, by decoupling the control and separately controlling the two axes, one can simplify the mathematics.
A second important reason to be able to de-couple the control about the pointing direction is that one typically has feedback systems that measure the position of the optical axis. Upon detecting which way the optical axis is moving one needs a feedback system including transducers to correct the pointing direction.
It is noted that feedback sensors inform one of what errors there are in the pointing direction. If these sensors are placed on the two orthogonal axes they measure error in these axial directions. Having measured errors along these axes, then movements of the actuators on these two axes may be easily controlled by the error signals.
Thus, if one measures the errors on the same axes as those utilized for the transduction of the pointing direction, then feedback systems are greatly simplified.